Climate Change Mitigation Game with Group Size 10, Heterogeneity, and Medium Thr

Question

Climate Change Mitigation Game with
Group Size 10, Heterogeneity, and Medium Threat Level YOU ARE A HIGH INCOME COUNTRY

You will be randomly grouped with nine other students in this class to form a group of size 10. PERIOD ONE

Each student represents a country with a potential income, except that this time around countries differ in their potential incomes, which equal 10 each for the three low income countries L, 50 each for the four middle income countries M, and 90 each for the three high income countries H:

yL = yL = yL = 10
yM = yM = yM = yM = 50 yH = yH = yH = 90

In this play of the game, YOU ARE A HIGH INCOME COUNTRY.

Each country can choose to realize an income lower than its potential so as to reduce the probability of catastrophic climate change.

Let

Explanation / Answer

Total maximum possible income=3*10+4*50+2*90+choice=choice+410

we do not know the choice of the other players, hence we take as their choice, the expectation. The expectation when the choice is uniform is half of the maximum potential, that is 5 for low income, 25 for medium and 45 for high. So the total expectation of these countries is 205=410/2.

Total revenue=choice+205 if revenue<45, so it makes sense to choose choice=44, which gives revenue=249

Total revenue=(1-p)*(choice+205)+p*0 if revenue>=45, so it makes sense to choose choice=90, which gives (1-p)*295

which is bigger, 249 or (1-p)*295?

249<(1-p)*295 is equivalent to 1-p>249/295 or p<46/295

So it depends on p, if p is known and p<46/295 choose income=44 and if p>46/295 choose income=90. If p=46/295, choose either 44 or 90. If p is unknown, take p=1/2 as expectation, so by above, pick income=90

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